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In recent years, electrification of powertrains has been promoted to improve fuel efficiency and CO2 emissions. Along with electrification, it is possible to reduce engine usage frequency and improve the fuel efficiency in traveling. Especially in a hybrid electric vehicle (HEV), the state changes from motor assist mode to engine firing mode. As a result, stay time in eigenvalue of a powertrain is shortened, and vibration of the vehicle body at the engine start situation is able to be reduced as compared with conventional engine-driven vehicle. However, since the HEV is equipped with a high compression ratio engine for improving fuel economy, there is cause for concern that excitation force generated by the powertrain at the time of engine start increases. Also, the vehicle body vibration at engine start situations requires further consideration, because the operation frequency of engine decreases.